78.1.18 problem 2 (d)

Internal problem ID [18073]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (d)
Date solved : Tuesday, January 28, 2025 at 11:25:29 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\arcsin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(diff(y(x),x)=arcsin(x),y(x), singsol=all)
 

\[ y = x \arcsin \left (x \right )+\sqrt {-x^{2}+1}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 23

DSolve[D[y[x],x]==ArcSin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \arcsin (x)+\sqrt {1-x^2}+c_1 \]